Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/44218
Title: Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Authors: Pang, J.-S.
Sun, D. 
Sun, J. 
Keywords: Complementarity problem
Lorentz cone
Semidefinite cone
Variational inequality
Issue Date: 2003
Source: Pang, J.-S.,Sun, D.,Sun, J. (2003). Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems. Mathematics of Operations Research 28 (1) : 39-63. ScholarBank@NUS Repository.
Abstract: Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone.
Source Title: Mathematics of Operations Research
URI: http://scholarbank.nus.edu.sg/handle/10635/44218
ISSN: 0364765X
Appears in Collections:Staff Publications

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